Integrated power and thermal management systems (IPTMS) may use an engine, such as a gas turbine engine, as a prime mover for an electric generator. In pulsed-power applications of such systems, rapid application of mechanical load on the engine's output shaft can cause the speed of the output shaft to droop (or drop) to undesirable levels before an engine fuel controller may respond and restore the speed of the engine's output shaft. Typical fuel controllers for such engines are designed to monitor the output shaft speed and adjust fuel flow to the generator in order to try to maintain the output shaft speed at a constant speed. Such fuel controllers react to the reduction in output shaft speed by increasing fuel flow to the engine. If the prime mover is a multi-shaft gas turbine engine, the increased fuel, which is burnt in the combustor to increase the energy of the fluid stream, first acts on the inner shaft(s) to increase the speed of the inner shaft(s) and, correspondingly, on the energy of an output flow of the gas turbine engine. This increased energy is seen eventually by the output shaft of the engine, which causes an increase in the output power and thus restores the output shaft speed to the constant speed. There is naturally a lag, not only in the time that it takes the fuel controllers to detect the decrease in output shaft speed and respond by increasing the fuel flow, but also in the time between increasing the fuel flow and having the increase in useful energy arrive at the output shaft.